Up to now, various flat shell’s elements are created by combining plane and bending plate elements. In the case of complicated problems with coarse distorted mesh, only using efficient element leads to the accurate responses. These kinds of the elements are insensitive to the distortion. In fact, they can identify and remove the related errors. In this paper, two internal and boundary fields are deployed in a hybrid functional for formulating the proposed plane element. The method is established based on the optimum strain states. Furthermore, Trefftz functionals for independent internal and boundary fields are employed to formulate the suggested bending element. In this procedure, the optimum strain states construct the internal field, and element’s boundary field is achieved by considering the beam behavior. Finally, the high efficiency of author’s element is assessed by solving several numerical samples.

Keywords